The barest mention of Dragons’ Den sets Isaac Lilos racing up the stairs from the basement office of his shop, Arty Globe, in the corner of Greenwich Market.

If customers want to know about the 39-year-old’s experience on the popular television show, he’ll regale them, at length, on just why his pitch flopped.

Hartwig Braun — the Israeli entrepreneur’s 45-year-old partner, both professionally and personally — sniggers as Lilos explains how he had always thought it would be “wonderful” to be in the Den, how “in my mind there would be a bidding war to invest” in his grand plans.

Instead, Lilos went through “a humbling lesson” when he faced Duncan Bannatyne et al back in April 2009, suffering from exhaustion as he was also preparing to open the shop later that month. “I hadn’t slept and then we waited 12 hours to go in. We even had to ask permission to go to the toilet so we wouldn’t meet people who had already pitched. When I went in, my [internal] battery died, even my reserve battery,” he sighs.

The Dragons pulled apart the duo’s plans to incorporate Braun’s hand-drawn, digitally coloured 3-D cityscapes on Oyster Card wallets, mugs, cuff links and mouse mats. Still, the previous summer the pair were dragging four large suitcases full of greetings cards and postcards from their home in Nottingham as they lost £300 on a trial stall at Covent Garden’s Jubilee Market; by April they had relocated to a buzzing, artisan area of South-east London and were in effect advertising for nothing on the BBC.

The snub appears to be one of the Dragons’ costlier mistakes, as the budding entrepreneurs have made £600,000 in four years, and are planning selectively to place their products with big-name stores.

Another couple of Arty Globe stores are being considered, and silk scarves decorated with the couple’s distinctive curved fish-eye lens panoramas of London sell for £199 a pop.

The distorted designs, which are detailed enough to include what in real life are nondescript office blocks as well as landmarks such as the London Eye, are not only loved by tourists. There is bespoke work for the likes of easyJet, which sells the pair’s 54-piece jigsaws on its flights. Hamleys hired Braun to draw the toyshop for its 250th anniversary in 2010, and the Guggenheim Museum in Bilbao sells Arty Globe merchandise in its souvenir shop. The government of Texas recently came calling, quite literally, as one of its marketing team door-stepped them to discuss how Arty Globe could help to promote the American state around the world.

Lilos is the business brain, having “pestered” Braun to quit a dull job in architecture. He would redraw the same building 15 times, as clients demanded more and more floorspace be squeezed into a tight location. Lilos wanted to commercialise the creative genius of his “doodles”.

Braun wasn’t convinced: “It’s not easy to give up something you’ve studied for so long — seven years to become an architect — despite the frustrations. It was not such a quick decision.”

“The thing is, he’s German, everything’s a discussion,” laughs Lilos. “He couldn’t see the opportunity that I could see.”

Braun’s caution was understandable. Lilos had made mistakes in business, with a Lincolnshire-based car venture that was an early victim of the financial crisis.

Lilos, who moved from Israel in 1997 to help his brother run a family property business, was selling vehicles to both trade and the public, but had put too much money into stock. He had also been romantically involved with his then-business partner, a situation that later made managing the company difficult: “I had split up with my partner, and it wasn’t that amicable, but we stayed together as a business.”

Now, he wanted to do the same thing again with the man he had fallen for in a Paris bar in 2003.

“I was over from Berlin helping a friend renovate a flat,” smiles Braun. “I didn’t really end up helping my friend that much.”

Braun soon moved to the UK, and Lilos discovered a Christmas card that the bored architect had drawn of Amsterdam a few years earlier. Braun had been toying with “deliberately breaking the rules of perspective” and even as a schoolchild he was illustrating his biology and geography textbooks with wacky designs.

It took a while but Braun eventually gave in to Lilos’s badgering and spent several months drawing a 1.5-metre canvas called “London looking north”. This became the basis of a business that has now sold more than 150,000 products. How the Dragons must be kicking themselves.